The retired Marine Corps general also said “civilian casualties are a fact of life in this sort of situation”, adding: “We’re not the perfect guys, but we are the good guys. And so we’re doing what we can.”

His remarks came a day after he cited the suicide bombing in Manchester, which has been claimed by Isis, in a speech to graduating cadets at the United States Military Academy at West Point.

“Manchester’s tragic loss underscores the purpose of your years of study and training at this elite school,” Mattis said on Saturday. “We must never permit murderers to define our time or warp our sense of normal. This is not normal.”

The bombing outside an Ariana Grande concert at Manchester Arena killed 22 people, the youngest an eight-year-old girl, and injured dozens more. Fourteen people have been arrested, with two subsequently released. The bomber, Salman Abedi, had been to Libya and may have traveled to Syria.

Speaking on CBS’s Face the Nation on Sunday, Mattis said: “Our strategy right now is to accelerate the campaign against Isis. It is a threat to all civilized nations. And the bottom line is we are going to move in an accelerated and reinforced manner, throw them on their back foot.

“We have already shifted from attrition tactics, where we shove them from one position to another in Iraq and Syria, to annihilation tactics where we surround them. Our intention is that the foreign fighters do not survive the fight to return home to North Africa, to Europe, to America, to Asia, to Africa. We’re not going to allow them to do so. We’re going to stop them there and take apart the caliphate.”

Mattis also said efforts against Isis would be “a long fight” and “a fight about ideas”.

“We’re going to shatter their sense of invincibility there in the physical caliphate,” he said. “That’s only one phase of this. Then we have the virtual caliphate, that they use the internet.”

“We have got to dry up their recruiting,” he said. “We have got to dry up their fundraising. The way we intend to do it is to humiliate them, to divorce them from any nation giving them protection, and humiliating their message of hatred, of violence. Anyone who kills women and children is not devout. They … cannot dress themselves up in false religious garb and say that somehow this message has dignity.”

Asked if he was concerned by the prospect of civilian casualties caused by such aggressive action, Mattis said: “Civilian casualties are a fact of life in this sort of situation. We do everything humanly possible consistent with military necessity, taking many chances to avoid civilian casualties at all costs.”

Mosul's children were shouting beneath the rubble. Nobody came

Read more

“The American people and the American military will never get used to civilian casualties,” Mattis said. “And we will – we will fight against that every way we can possibly bring our intelligence and our tactics to bear.

“People who have had tried to leave that city were not allowed to by Isis. We are the good guys. We’re not the perfect guys, but we are the good guys. And so we’re doing what we can.”

Regarding the civilian deaths in Mosul, Mattis said: “We believe we found residue that was not consistent with our bomb. So we believe that what happened there was that Isis had stored munitions in a residential location. Showing, once again, the callous disregard that has characterized every operation they have run.”

Mattis, who has been nicknamed “Mad Dog” due to his preference for aggressive tactics, was also asked: “What keeps you awake at night?”

“Nothing,” he said. “I keep other people awake at night.”

• This article was amended on 29 May 2017 because an earlier version incorrectly referred to Salman Abedi as Libyan.